SBE SS3 Secure

STEEL BUILDINGS IN EUROPE Single-Storey Steel Buildings Part 3: Actions

Single-Storey Steel Buildings Part 3: Actions

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Part 3: Actions

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FOREWORD This publication is part three of a design guide, Single-Storey Steel Buildings.

The 10 parts in the Single-Storey Steel Buildings guide are: Part 1: Architects guide Part 2: Concept design Part 3: Actions Part 4: Detailed design of portal frames Part 5: Detailed design of trusses Part 6: Detailed design of built up columns Part 7: Fire engineering Part 8: Building envelope Part 9: Introduction to computer software Part 10: Model construction specification Part 11: Moment connections

Single-Storey Steel Buildings is one of two design guides. The second design guide is Multi-Storey Steel Buildings.

The two design guides have been produced in the framework of the European project Facilitating the market development for sections in industrial halls and low rise buildings (SECHALO) RFS2-CT-2008-0030.

The design guides have been prepared under the direction of Arcelor Mittal, Peiner Trger and Corus. The technical content has been prepared by CTICM and SCI, collaborating as the Steel Alliance.

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Part 3: Actions

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Contents Page No

FOREWORD iii

SUMMARY vi

1 INTRODUCTION 1

2 SAFETY PHILOSOPHY ACCORDING TO EN 1990 2 2.1 General format of the verifications 2 2.2 Ultimate limit states and serviceability limit states 2 2.3 Characteristic values and design values of actions 3

3 COMBINATIONS OF ACTIONS 4 3.1 General 4 3.2 ULS combinations 4 3.3 SLS combinations 6

4 PERMANENT ACTIONS 8

5 CONSTRUCTION LOADS 9

6 IMPOSED LOADS 10 6.1 General 10 6.2 Actions induced by cranes according to EN 1991-3 10 6.3 Horizontal loads on parapets 15

7 SNOW LOADS 16 7.1 General 16 7.2 Methodology 16

8 WIND ACTIONS 22 8.1 General 22 8.2 Methodology 22 8.3 Flowcharts 31

9 EFFECT OF TEMPERATURE 32

REFERENCES 33

Appendix A Worked Example: Snow load applied on a single-storey building 35

Appendix B Worked Example: Wind action on a single-storey building 45

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SUMMARY This document provides guidelines for the determination of the actions on a single-storey building according to EN 1990 and EN 1991. After a short description of the general format for limit state design, this guide provides information on the determination of the permanent loads, the variable actions and the combinations of actions. The determination of the snow loads and the calculation of the wind action are described and summarized in comprehensive flowcharts. Simple worked examples on the snow loads and the wind action are also included.

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1 INTRODUCTION

This guide provides essential information on the determination of the design actions on a single-storey building. It describes the basis of design with reference to the limit state concept in conjunction with the partial factor method, according to the following parts of the Eurocodes:

x EN 1990: Basis of structural design[1]. x EN 1991: Actions on structures

- Part 1-1: General actions Densities, self-weight, imposed loads for buildings[2].

- Part 1-3: General actions Snow loads[3] - Part 1-4: General actions Wind actions[4] - Part 1-5: General actions Thermal actions[5] - Part 3: Actions induced by cranes and machinery.[6]

The guide is a comprehensive presentation of the design rules applied to single-storey buildings with reference to the appropriate clauses, tables and graphs of the Eurocodes.

Additional information can be found in the references [7][8].

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2 SAFETY PHILOSOPHY ACCORDING TO EN 1990

2.1 General format of the verifications A distinction is made between ultimate limit states (ULS) and serviceability limit states (SLS).

The ultimate limit states are related to the following design situations:

x Persistent design situations (conditions of normal use) x Transient design situations (temporary conditions applicable to the

structure, e.g. during execution, repair, etc.)

x Accidental design situations (exceptional conditions applicable to the structure)

x Seismic design situations (conditions applicable to the structure when subjected to seismic events). These events are dealt within EN 1998[9], and are outside the scope of this guide.

The serviceability limit states concern the functioning of the structure under normal use, the comfort of people and the appearance of the construction.

The verifications shall be carried out for all relevant design situations and load cases.

2.2 Ultimate limit states and serviceability limit states 2.2.1 Ultimate limit states (ULS)

The states classified as ultimate limit states are those that concern the safety of people and /or the safety of the structure. The structure shall be verified at ULS when there is:

x Loss of equilibrium of the structure or any part of it (EQU) x Failure by excessive deformation, rupture, loss of stability of the structure

or any part of it (STR)

x Failure or excessive deformation of the ground (GEO) x Failure caused by fatigue or other time-dependent effects (FAT).

2.2.2 Serviceability Limit States (SLS) The structure shall be verified at SLS when there is:

x Deformations that affect the appearance, the comfort of users or the functioning of the structure

x Vibrations that cause discomfort to people or that limit the functional effectiveness of the structure

x Damage that is likely to adversely affect the appearance, the durability or the functioning of the structure.

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2.3 Characteristic values and design values of actions

2.3.1 General Actions shall be classified by their variation in time as follows:

x Permanent actions (G), e.g. self-weight of structures, fixed equipment, etc. x Variable actions (Q), e.g. imposed loads, wind actions, snow loads, etc. x Accidental actions (A), e.g. explosions, impact from vehicles, etc. Certain actions may be considered as either accidental and/or variable actions, e.g. seismic actions, snow loads, wind actions with some design situations.

2.3.2 Characteristic values of actions The characteristic value (Fk) of an action is its principal representative value. As it can be defined on statistical bases, it is chosen so as to correspond to a prescribed probability of not exceeding on the unfavourable side, during a reference period taking into account the design working life of the structure.

These characteristic values are specified in the various Parts of EN 1991.

2.3.3 Design values of actions The design value Fd of an action F can be expressed in general terms as:

Fd = Jf \ Fk where:

Fk is the characteristic value of the action

Jf is a partial factor for the action \ is either 1,00, \0, \1 or \2

2.3.4 Partial factors Partial factors are used to verify the structures at ULS and SLS. They should be obtained from EN 1990 Annex A1, or from EN 1991 or from the relevant National Annex.

2.3.5 \ factors In the combinations of actions, \factors apply to variable actions in order to take into account the reduced probability of simultaneous occurrence of their characteristic values.

The recommended values for \factors for buildings should be obtained from EN 1990 Annex A1 Table A1.1, or from EN 1991 or from the relevant National Annex.

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3 COMBINATIONS OF ACTIONS

3.1 General The individual actions should be combined so as not to exceed the limit state for the relevant design situations.

Actions that cannot occur simultaneously, e.g. due to physical reasons, should not be considered together in a same combination.

Depending on its uses and the form and the location of a building, the combinations of actions may be based on not more than two variable actions See Note 1 in EN 1990 A1.2.1(1). The National Annex may provide additional information.

3.2 ULS combinations 3.2.1 Static equilibrium

To verify a limit state of static equilibrium of the structure (EQU), it shall be ensured that:

Ed,dst Ed,stb where:

Ed,dst is the design value of the effect of destabilising actions Ed,stb is the design value of the effect of stabilising actions

3.2.2 Rupture or excessive deformation of an element To verify a limit state of rupture or excessive deformation of a section, member or connection (STR and/or GEO), it shall be ensured that:

Ed Rd where:

Ed is the design value of the effect of actions Rd is the design value of the corresponding resistance

Each combination of actions should include a leading variable action or an accidental action.

3.2.3 Combinations of actions for persistent or transient design situations According to EN 1990 6.4.3.2(3), the combinations of actions can be derived either from expression (6.10) or from expressions (6.10a and 6.10b whichever is more onerous). The choice between these two sets of expressions may be imposed by the National Annex.

In general, expression (6.10) is conservative in comparison to the pair of expressions (6.10a and 6.10b), but it leads to a reduced number of combinations to consider.

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Permanent actions Leading

variable action Accompanying variable actions

Ed = t1 jk,jG,j GJ + k,1Q,1QJ + !1 ik,i0,iQ,i Q\J (6.10)

Ed = t1 jk,jG,j GJ + k,1Q,10,1 QJ\ + !1 ik,i0,iQ,i Q\J (6.10a)Ed = t1 jk,jG,j GJ[ + k,1Q,1QJ + !1 ik,i0,iQ,i Q\J (6.10b)

Gk and Qk are found in EN 1991 or its National Annex.

JG and JQ are found in Table A1.2(A) for static equilibrium (EQU); Tables A1.2(B) and A1.2(C) for rupture (STR and/or GEO) of EN 1990 or in the National Annex. Table 3.1 gives the recommended values of the partial factors.

Table 3.1 Recommended values of partial factors

Table (EN 1990) Limit state JGj,inf JGj,sup JQ,1 = JQ,I JQ,1 = JQ,I

A1.2(A) EQU 0,90 1,10 1,50 1,50

A1.2(B) STR/GEO 1,00 1,35 1,50 1,50

A1.2(C) STR/GEO 1,00 1,00 1,30 1,30

\0 factors are found in EN 1990 Table A1.1 or in its National Annex. This factor varies between 0,5 and 1 except for roofs of category H (\0 = 0). is a reduction factor for permanent loads. According to EN 1990 Table A1.2(B), the recommended value for buildings is = 0,85. The National Annex may specify a different value.

For example, according to expression 6.10:

1. With snow as the leading variable action:

Ed = 1,35 G + 1,5 S + (1,5 u 0,6) W = 1,35 G + 1,5 S + 0,9 W 2. With wind as the leading variable action:

Ed = 1,35 G + 1,5 W + (1,5 u 0,5) S = 1,35 G + 1,5 W + 0,75 S 3.2.4 Combinations of actions for accidental design situations

Combinations of actions for accidental design situations should either involve an explicit accidental action or refer to a situation after an accident event.

Permanent actions Accidental

action Leading variable

action Accompanying variable actions

Ed = t1 jk,j G + Ad + ( 1,1\ or 2,1\ ) k,1Q + !1 ik,i0,iQ,i Q\J

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The choice between \1,1Qk,1 or \2,1Qk,1 should be related to the relevant accidental design situation. Guidance is given in EN 1990 or in the National Annex to EN 1990.

3.3 SLS combinations 3.3.1 Serviceability Limit State

To verify a serviceability limit state, it shall be ensured that:

Ed Cd where:

Ed is the design value of the effects of actions specified in the serviceability criterion,

Cd is the limiting design value of the relevant serviceability criterion.

3.3.2 Characteristic combination The characteristic combination is normally used for irreversible limit states.



Ed = t1 jk,j G + k,1Q + !1 ik,i0,i Q\ For example:

Ed = G + S + 0,6 W

Ed = G + W + 0,5 S

3.3.3 Frequent combination The frequent combination is normally used for reversible limit states.



Ed = t1 jk,j G + k,11,1Q\ + !1 ik,i2,i Q\ For example:

Ed = G + 0,2 S (\2 = 0 for the wind action) Ed = G + 0,2 W (\2 = 0 for the snow load)

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3.3.4 Quasi-permanent combination The quasi-permanent combination is normally used for long-term effects and the appearance of the structure.

Permanent actions Variable actions

Ed = t1 jk,j G + !1 ik,i2,i Q\ For example:

Ed = G (since \2 = 0 for both the wind action and the snow load)

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4 PERMANENT ACTIONS

The self-weight of construction works is generally the main permanent load. It should be classified as a permanent fixed action. In most cases, it should be represented by a single-characteristic value.

The total self-weight of structural and non-structural members, including fixed services, should be taken into account in combinations of actions as a single action.

Non-structural elements include roofing, surfacing and coverings, partitions and linings, hand rails, safety barriers, parapets, wall claddings, suspended ceilings, thermal insulation, fixed machinery and all fixed services (heating, ventilating, electrical and air conditioning equipment, pipes without their contents, cable trunking and conduits).

The characteristic values of self-weight should be defined from the dimensions and densities of the elements.

Values of densities of construction materials are provided in EN 1991-1-1 Annex A (Tables A.1 to A.5).

For example:

Steel: J = 77,0 to 78,5 kN/m3 Aluminium: J = 27,0 kN/m3 For manufactured elements (faades, ceilings and other equipment for buildings), data may be provided by the manufacturer.

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5 CONSTRUCTION LOADS

EN 1991-1-6 gives rules for the determination of the actions during execution. Verifications are required for both serviceability limit states and ultimate limit states.

Table 4.1 defines construction loads that have to be taken into account:

x Personnel and hand tools (Qca) x Storage of movable items (Qcb) x Non permanent equipment (Qcc) x Moveable heavy machinery and equipment (Qcd) x Accumulation of waste material (Qce) x Loads from parts of structure in a temporary state (Qcf). Recommended values are provided in the same table but values may be given in the National Annex.

In single-storey buildings, an example of construction load would be the weight of cladding bundles on the structure prior to fitting.

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6 IMPOSED LOADS

6.1 General Generally, imposed loads on buildings shall be classified as variable actions. They arise from occupancy. They include normal use by persons, furniture and moveable objects, vehicles, anticipating rare events (concentrations of persons or of furniture, momentary moving or stacking of objects, etc.). Movable partitions should be treated as imposed loads.

Imposed loads are represented by uniformly distributed loads, line loads or point loads applied on roofs or floors, or a combination of these loads.

Floor and roof areas in buildings are sub-divided into categories according to their use (EN 1991-1-1 Table 6.1). The characteristic values qk (uniformly distributed load) and Qk (concentred load) related to these categories are specified in EN 1991-1-1 Table 6.2 or in the relevant National Annex.

For the design of a single floor or a roof, the imposed load shall be taken into account as a free action applied at the most unfavourable part of the influence area of the action effects considered.

For imposed loads for floors and accessible roofs, the characteristic value qk may be multiplied by reduction factors due to the loaded area and the number of storeys (EN 1991-1-1 6.3.1.2). More information is provided in Section 6 of Multi-storey steel buildings. Part 3: Actions[10].

Characteristic values of imposed loads are specified in EN 1991-1-1 Section 6.3 as follows:

6.3.1 Residential, social, commercial and administration areas

6.3.2 Areas for storage and industrial activities

6.3.3 Garages and vehicle traffic areas

6.3.4 Roofs.

6.2 Actions induced by cranes according to EN 1991-3

6.2.1 General Most industrial buildings have to be equipped with handling devices to allow movement and carriage of loads through the building. A typical crane used in industrial buildings is shown in Figure 6.1 with the main technical terms.

One of the convenient solutions is the installation of cranes. The structure is subject to loads acting both vertically and laterally. Such actions can become the dominant ones for the structure.

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The determination of the actions induced by cranes is complex, as they include many parameters such as:

x Weight of the crane and safe working load x Stiffness of both the crane structure and the runway girders x Speed and acceleration of the crane x Design of the crane (wheel drives, guidance systems, etc.). The characteristics of the crane generally have to be supplied by the crane manufacturers.

2

3

4

5

6

1

2

7

7

77

1

8

8

1 Axis of wheels 2 Bogies 3 Main girders of the crane 4 Crab

5 motor drive unit 6 Hook 7 Axes of runway beams 8 Axis of track wheels

Figure 6.1 Main components of a crane

The relevant standard which specifies these actions is EN 1991-3 Actions on structures Actions induced by cranes and machinery.

The variable crane actions are separated into:

x Variable vertical crane actions caused by self weight of the crane and the hoist load

x Variable horizontal actions caused by acceleration or deceleration or by skewing or other dynamic effects.

6.2.2 Vertical actions Vertical actions include dead loads (self weight of the crane, safe working load, hook block, etc.)

The distribution of these dead loads is generally assumed on the basis of simply supported beams, considering both the main girders and the secondary beams over the bogies.

Two positions of the crab are generally considered to obtain the worst load arrangement on the crane runway: crab located in the middle of the crane span or crab located at the minimum distance of hook approach from the runway.

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Considering both crab positions leads to the maximum and minimum loads per wheel acting on the crane runway.

An eccentricity of application for these loads, generally taken as of the rail head, also has to be considered.

In order to consider some features such as impact of wheels at rail joints, wear of rail and wheels, release or lifting of the working load etc., dynamic factors are applied to the above static action values.

For vertical action, the dynamic factors are called M1 to M4 (refer to Table 2.4 of EN 1991-3).

6.2.3 Horizontal actions The following types of horizontal forces should be taken into account:

x Horizontal forces caused by acceleration and deceleration of the crane in relation to its movement along the runway beams

x Horizontal forces caused by acceleration and deceleration of the crab in relation to its movement along the crane bridge

x Horizontal forces caused by skewing of the crane in relation to its movement along the runway beam

x Buffer forces related to crane movement x Buffer forces related to movement of the crab. Only one of the 5 types of the above horizontal forces should be considered at the same time. The third one is generally assumed to be covered by the fifth one. The two last ones are considered as accidental forces.

The following details considering the first two types are generally those that lead to dimensioning configurations for the crane runway:

1. Forces that result from acceleration and deceleration of the crane along its crane way.

They act at the contact surface between the rail and the wheel. They have to be amplified by a dynamic factor M5 (see Table 2.6 of EN 1991-3) whose value may vary from 1,0 to 3,0, the value 1,5 being generally relevant. These forces consist of longitudinal forces (K1 and K2) and transverse forces (HT,1 and HT,2) as shown in Figure 6.2. The longitudinal forces correspond to the resultant drive force K; such force must be transmitted through the driven wheels without skidding even when the crane carries no working load.

The resultant of the drive force does not pass through the centre of mass S, generating a couple that causes a skewing moment each time the crane accelerates or brakes. This moment is distributed on each runway according to their distance from the centre of mass.

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1 2

l

[1 l [2 l

HT,1

HT,1

HT,2

HT,2

K1 K2 K=K1+K2

S M

ls 3 3

1 Rail 2 Rail 3 Driven wheels

Figure 6.2 Acceleration forces

2 Forces that result from skewing of the crane in relation to its movement along the runway beam

The forces described hereunder are due to the oblique travel of the crane when it assumes a skew position, for any reason, and then continues obliquely until the guidance mean comes in contact with the side of the rail.

The lateral force on the side of the rail increases to reach a peak value S; due to the action of this force, the crane returns to its proper course, at least temporarily.

Guidance systems can be either specific guide roller or the flanges of the track wheels.

The calculation of the corresponding forces depends on the type of drive system (drive units without synchronisation of the driven track wheels or central drive unit coupled to the wheels), the fixing of wheels according to lateral movement and the location of the instantaneous centre of rotation.

Forces resulting from skewing consist of longitudinal and transverse forces such as indicated in Figure 6.3.

These loads act at each wheel (HS,i,j,k) and a guide force S (also called steering force) acts at the guidance system.

In the forces HS,i,j,k the indexes refer to:

x S for skewing x i for beam runway x j for wheel pair (the number 1 refers to the farthest from the centre of

rotation)

x k for direction of the force, L if acting longitudinally or T if acting transversally.

The force S equilibrates the sum of the transverse forces.

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i=1

x

h HS,2,j,T

y

HS,2,j,L HS,1,j,L

HS,1,j,T a e

xt

e j

i=2

j

D

[1 l [2 l 1

1

x 2

3

i = 1

HS,1,1,T

6

i = 2

j = 1

j = 2 HS,1,2,T

HS,2,1,T

HS,2,2,T

HS,1,2,L HS,2,2,L

4

5

DS

1 Guidance system 2 Direction of motion 3 Instantaneous centre of

rotation D is the skew angle i = Rails j = Pairs of wheels

Figure 6.3 Forces resulting from skewing

6.2.4 Other loads or forces To give an overall picture of the loads induced by cranes, it is necessary to mention:

1. The wind actions on the structure of the crane and on the payload The wind is generally considered at a speed of 20 m/s if considered together with the payload (external use).

2. Test loads - Dynamic test load: at least 110% of the nominal hoist load, amplified by

a dynamic factor M6 (see EN 1991-3 2.10 (4)). - Static test load: at least 125% of the nominal hoist load without dynamic

factor.

3. Accidental forces - Tilting force: when the load or lifting attachments collides with an

obstacle.

- And if relevant: Mechanical failure (failure of a single brake, wheel axle failure, etc.).

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6.2.5 Multiple crane action There is often more than one crane in one building; they can move either on the same runway or on several levels in a same bay or in multi-bay buildings.

Multiple cranes have to be considered in the most unfavourable position for:

x The crane runway x The supporting structure. Table 6.1 Recommended maximum number of cranes to be considered in

the most unfavourable position Cranes to

each runway Cranes in each

shop bay Cranes in

multi-bay buildings

Crane action

Vertical 3 4 4 2

Horizontal 2 2 2 2

For horizontal crane actions, it is acceptable to limit the number of cranes acting with their payload to two; for vertical actions, the number of cranes varies from two to four.

The cranes which are unloaded have nevertheless to be considered, if unfavourable.

6.3 Horizontal loads on parapets The characteristic values of the line loads qk acting at the height of the partition walls or parapets but not higher than 1,20 m should be taken from EN 1991-1-1 Table 6.12 or from the National Annex.

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7 SNOW LOADS

7.1 General This document gives guidance to determine the values of loads due to snow to be used for a typical single-storey building according to EN 1991-1-3. The design procedure is summarized in a flowchart (Figure 7.5). A worked example dealing with the determination of the snow loads on a single-storey building is given in Appendix A.

The guidance does not apply to sites at altitudes above 1500 m (unless otherwise specified).

Snow loads shall be classified as variable, fixed actions, unless otherwise stated in EN 1991-1-3. For particular conditions like exceptional snow loads and/or loads due to exceptional snow drifts, they may be treated as accidental actions depending on geographical locations.

Snow loads should be classified as static actions.

Two design situations may need to be considered:

x Transient/persistent situation should be used for both the undrifted and drifted snow load arrangements for locations where exceptional snow falls and exceptional snow drifts are unlikely to occur.

x Accidental design situation should be used for geographical locations where exceptional snow falls and/or exceptional snow drifts are likely to occur.

The National Annex may define which design situation to apply.

7.2 Methodology 7.2.1 Snow load on the ground

Different climatic conditions will give rise to different design situations. The possibilities are:

x Case A: Normal case (non exceptional falls and drifts) x Case B1: Exceptional falls and no exceptional drifts x Case B2: Exceptional drift and no exceptional falls (in accordance with

EN 1991-1-3 Annex B)

x Case B3: Exceptional falls and exceptional drifts (in accordance with EN 1991-1-3 Annex B)

The National Authority may choose the case applicable to particular locations for their own territory.

The National Annex specifies the characteristic value sk of snow load on the ground to be used.

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For locations where exceptional snow loads on the ground can occur, they may be determined by:

sAd = Cesl sk where:

sAd is the design value of exceptional snow load on the ground for the given location

Cesl is the coefficient for exceptional snow loads (the recommended value is = 2,0)

sk is the characteristic value of snow load on the ground for the given location.

The National Annex may recommend another value of Cesl, or the design value of exceptional snow load on the ground sAd.

7.2.2 Snow load on roofs The load acts vertically and refers to a horizontal projection of the roof area. Snow can be deposited on a roof in many different patterns.

Two primary load arrangements shall be taken into account:

x Undrifted snow load on roofs x Drifted snow load on roofs. Snow loads on roofs are derived from the snow loads on the ground, multiplying by appropriate conversion factors (shape, exposure and thermal coefficients). They shall be determined as follows:

x Persistent (conditions of normal use)/transient (temporary conditions) design situations:

s = Pi Ce Ct sk x Accidental (exceptional conditions) design situations where exceptional

snow load is the accidental action:

s = Pi Ce Ct sAd x Accidental design situations where the accidental action is the exceptional

drift and where EN 1991-1-3 Annex B applies:

s = Pi sk where:

Pi is the snow shape coefficient. It depends on the angle of pitch of roof D (Table 6.1)

Ce is the exposure coefficient (Ce = 1,0 is the default value) Ct is the thermal coefficient (Ct 1; Ct = 1,0 is the default value).

The National Annex may give the conditions of use for Ce and Ct.

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Table 7.1 Snow load shape coefficients

Angle of pitch of roof D 0 d D d 30 30 < D < 60 D t 60 P1 0.8 0.8 (60 D)/30 0 P2 0.8 + 0.8 D/30 1.6 -

These values P1 and P2 apply when the snow is not prevented from sliding off the roof (no snow fences or other obstructions like parapets). If obstructions exist, the snow load shape coefficient should not be reduced below 0.8.

The snow load shape coefficient that should be used for monopitch roofs is shown in Figure 7.1, where P1 is given in Table 7.1. The load arrangement should be used for both the undrifted and drifted load arrangements.

D

P1(D)

Figure 7.1 Snow load shape coefficient Monopitch roof

The snow load shape coefficients that should be used for pitched roofs are shown in Figure 7.2, where P1 is given in Table 7.1. Case (i) corresponds to the undrifted load arrangement.

Cases (ii) and (iii) correspond to the drifted load arrangements.

PD

0,5 PD)

PD

PD

PD) PD

D1 D2

(i)

(ii)

(iii)

(i) Undrifted load arrangement (ii) and (iii) Drifted load arrangement

Figure 7.2 Snow load shape coefficient Pitched roof

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The snow load shape coefficients that should be used for multi-span roofs are shown in Figure 7.3, where P1 and P2 are given in Table 7.1. Case (i) corresponds to the undrifted load arrangement.

Case (ii) corresponds to the drifted load arrangement.

D1 D2

(i)

(ii)

PD P1 (D2) P1 (D1) P1 (D2)

D1 D2

P1 (D1) P2 [(D1+D2)/2] P1 (D2)

(i) Undrifted load arrangement

(ii) Drifted load arrangement

Figure 7.3 Snow load shape coefficient Multi-span roof

The snow load shape coefficients that should be used for roofs abutting to taller construction works are shown in Figure 7.4, where P1, P2, Ps, Pw are given by the following expressions:

P1 = 0,8 This value assumes that the lower roof is flat. If it is not, a specific study should be carried out by taking into account the direction of the slope.

P2 = Ps + Pw where:

Ps is the snow shape coefficient due to sliding of snow from the upper roof.

For D 15, Ps = 0 For D > 15, Ps = half the snow load on the adjacent slope of the

upper roof

Pw is the snow load shape coefficient due to wind Pw = (b1 + b2)/2h with Pw Jh / sk And the recommended range is (it may be given in the National

Annex):

0,8 Pw 4 b1, b2 and h are defined in Figure 7.4

J is the weight density of snow for this calculation (2 kN/m3)

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ls is the drift length determined as : ls = 2 h

The recommended limits of the drift length are (they may be given in the National Annex):

5 m ls 15 m If b2 < ls, the coefficient P2 is truncated at the end of the lower roof. The cases (i) corresponds to with the undrifted load arrangement.

The cases (ii) corresponds to with the drifted load arrangements.

D h

b2b1

h

b1 b2 < ls

D

(i)

(ii)

P1 (i)

(ii)P1

P1

P2 P2 Ps Ps

Pw Pw

ls ls

Figure 7.4 Snow load shape coefficient Roofs abutting to taller construction

works

7.2.3 Local effects The design situations to be considered are persistent/transient. EN 1991-1-3 Section 6 gives forces to be applied for the local verifications of:

x Drifting at projections and obstructions (EN 1991-1-3 6.2) x The edge of the roof (EN 1991-1-3 6.3) x Snow fences (EN 1991-1-3 6.4).

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7.2.4 Flowchart

Characteristic value of the snow load sk on the ground

Shape coefficients Pi

Location of the constructionNational map

Per

sist

ent /

tran

sien

t des

ign

situ

atio

ns

Snow load on the roof: s = PI Ce Ct sk

Acc

iden

tal d

esig

n si

tuat

ions

N

o dr

ift d

ue to

loca

l effe

ct

Exceptional load on the ground sAd = Cesl sk

Coefficient Cesl for exceptional snow load

Snow load on the roof: s = PI Ce Ct sAd

(including drifts, except local effects)

Exceptional drifts Snow load on the roof:

s = PI sk

Shape of the roof

Exposure coefficient Ce Thermal coefficient Ct

Location of the constructionNational map

National Annex

EN 1991-1-3 5.3

EN 1991-1-3 5.2(3) a)

EN 1991-1-3 Annex B

EN 1991-1-3 4.3

EN 1991-1-3 4.3

EN 1991-1-3 5.2(3) b)

Figure 7.5 Determination of the snow loads

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8 WIND ACTIONS

8.1 General This Section provides guidance to determine the values of the wind action to be used for the design of a typical single-storey building according to EN 1991-1-4. The design procedure is summarized by a flowchart in Figure 8.6 and Figure 8.7. A worked example dealing with the determination of the wind action on a single-storey building is given in Appendix B.

The rules apply to the whole structure or part of the structure, e.g. components, cladding units and their fixings.

A simplified set of pressures or forces whose effects are equivalent to the extreme effects of the turbulent wind represent the wind action.

Wind actions should be classified as variable fixed actions.

The relevant wind actions shall be determined for each design situation identified.

Where, in design, windows and doors are assumed to be shut under storm conditions, the effect of these being open should be treated as an accidental design situation.

8.2 Methodology The response of the structure to the effect of wind depends on the size, shape and dynamic properties of the structure. This response should be calculated from the peak velocity pressure qp and from the force and/or pressure coefficients.

8.2.1 Peak velocity pressure The peak velocity pressure qp(z) is the velocity pressure used in the calculations.

It depends on the wind climate, the reference height, the terrain roughness and orography. It is equal to the mean velocity pressure plus a contribution from short-term pressure fluctuations.

The peak velocity pressure can be calculated using the following procedure.

1. Fundamental value of the basic wind velocity vb,0 The fundamental value of the basic wind velocity is the characteristic 10 minutes mean wind velocity, irrespective of wind direction and time of year, at 10 m above ground level, in open country terrain. It corresponds to a mean return period of 50 years (annual probability of exceedence of 0,02).

The National Annex specifies the fundamental value of the basic wind velocity.

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2. Basic wind velocity vb vb = cdir cseason vb,0 where:

cdir is the directional factor cseason is the seasonal factor

The recommended value is 1,0 for both cdir and cseason but the National Annex may give other values.

3. Basic velocity pressure The basic velocity pressure qb is calculated as follows:

qb 2b 21 vU

where:

U is the air density = 1,25 kg/m3 (recommended value but the National Annex may give

another value)

4. Terrain factor kr 07,0

II,0

0r 19,0

zzk

where:

z0 is the roughness length according to the terrain category z0,II is the roughness length for the terrain category II: z0,II = 0,05 m zmax = 200 m

Terrain categories and terrain parameters are defined in EN 1991-1-4 Table 4.1, but the National Annex may give other values.

5. Roughness factor cr(z) cr(z) = kr ln(z/z0) for zmin z zmax cr(z) = cr(zmin) for z zmin

where:

z is the reference height defined by EN 1991-1-4 Figure 7.4. zmin depends on the terrain category, EN 1991-1-4 Table 4.1.

6. Orography factor co(z) The orography consists of the study of the shape of the terrain in the vicinity of the construction.

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The effects of orography may be neglected when the average slope of the upwind terrain is less than 3. The recommended value of co(z) is 1,0, but the National Annex may give the procedure to calculate the orography factor.

Annex A3 of EN 1991-1-4 gives the recommended procedure to determine co for hills, cliffs, etc.

7. Turbulence factor kl The recommended value is 1,0 but the National Annex may give other values.

8. Peak velocity pressure qp(z)

> @ )( 21)(71)( 2mvp zvzIzq U

where:

Iv(z) is the turbulence intensity which allows to take into account the contribution from short-term fluctuations

)/ln()(

)(0o

lv zzzc

kzI for zmin z zmax

)()( minvv zIzI for z < zmin zmax = 200 m vm(z) is the mean wind velocity at height z above the terrain: vm(z) = cr(z) co(z) vb

Alternative for step 8:

For single-storey-buildings, the determination of the mean wind velocity vm(z) is not absolutely necessary. The peak velocity pressure can be directly obtained from the exposure factor ce(z):

bep )()( qzczq where:

)( )()( )(

71)( 2r2o

ro

rle zczczczc

kkzc

For flat terrain (co(z) = 1) and for turbulence factor kl = 1, the exposure factor ce(z) can be directly obtained from Figure 4.2 of EN 1991-1-4, as a function of the height above terrain and a function of terrain category.

8.2.2 Wind pressure on surfaces Wind forces There are three types of wind forces acting on a building:

x External forces Fw,e (see 8.2.2.1) x Internal forces Fw,i (see 8.2.2.2) x Friction forces Ffr (see 8.2.2.3).

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The external and internal forces result in pressures perpendicular to the walls (vertical walls, roofs, etc.). By convention, pressure directed towards the surface is taken as positive, and suction, directed away from the surface as negative (Figure 8.1).

q < 0 q > 0

Figure 8.1 Sign convention for the pressure

As stated in EN 1991-1-4 5.3(2), the resulting wind force Fw acting on a structure, or a structural component, can be determined by the vector summation of Fw,e, Fw,i and Ffr. It can be globally expressed as follows:

Fw = cscd cf qp(ze) Aref

where:

cscd is the structural factor (for buildings with a height less than 15 m, it may be taken as 1)

Note: the mean wind velocity vm(z) is necessary to calculate the structural factor cscd.

cf is the force coefficient for the structure (or structural element) Aref is the reference area of the structure (or structural element). Here it

can be defined as the area of the projection of the structure or the structural component, on a vertical plan perpendicular to the wind direction.

Practical approach

In practice, the designer needs to evaluate the resulting pressure on the walls in order to determine the actions on the structural members. The resulting pressure can be expressed as follows:

Fw/Aref = cscd we wi

where:

we is the wind pressure acting on the external surface (see 7.2.1.2), wi is the wind pressure acting on the internal surface (see 7.2.1.3).

In addition the effects of the friction forces (see 7.2.1.4) have to be considered when necessary.

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8.2.2.1 External forces The external forces are obtained from:

surfaces

refedsew, AwccF

where:

cscd is the structural factor (see 7.2.1.1) we is the wind pressure acting on the external surface: we = qp(ze) cpe qp(ze) is the peak velocity pressure at the reference height ze ze is the reference height for the external pressure (generally, the height

of the structure). It depends on the aspect ratio h/b, where h is the height of the building and b is the crosswind dimension.

Generally, h is lower than b for single-storey buildings. In this case, ze is taken equal to the height of the building and the velocity pressure qp(z) is uniform on the whole structure: qp(ze) = qp(h).

cpe is the pressure coefficient for the external pressure. See 8.2.3 for vertical walls and 8.2.4 for roofs.

Aref is the reference area. Here it is the area of the surface under consideration for the design of the structure or the structural component.

8.2.2.2 Internal forces The internal forces are obtained from:

surfaces

refiiw, AwF

where:

wi is the wind pressure acting on the internal surface: wi = qp(zi) cpi zi is the reference height for the internal pressure (generally: zi = ze) qp(zi) is the peak velocity pressure at the height zi (generally: qp(zi) = qp(ze)) cpi is the pressure coefficient for the internal pressure, see 8.2.5.

8.2.2.3 Friction forces The friction force results from the friction of the wind parallel to the external surface. Friction is allowed for when the total area of all surfaces parallel to the wind is higher than four times the total area of all external surfaces perpendicular to the wind (windward and leeward), which is the case for long structures.

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W

d

b

h

Min(2b ; 4h)

Figure 8.2 Friction forces

The friction forces are obtained from:

frepfrfr AzqcF where:

cfr is the friction coefficient. It can be taken equal to: 0,01 for smooth surface (steel, smooth concrete, etc.)

0,02 for rough surface (rough concrete, tar-boards, etc.)

0,03 for very rough surface (ripples, ribs, folds, etc.).

qp(ze) is the peak velocity pressure at the reference height ze. Afr is the reference area. Friction forces are applied on the part of the

external surfaces parallel to the wind Afr, located beyond a distance from the upwind eaves or corners, equal to the smallest value of 2b or 4h, b and h as defined in Figure 8.2.

8.2.3 External pressure coefficients on vertical walls The values of the external pressure coefficients, given in tables in the Eurocode are attached to defined zones. The coefficients depend on the size of the loaded area A that produces the wind action in the zone under consideratiion. In the tables, the external pressure coefficients are given for loaded areas of 1 m2 (cpe,1) and 10 m2 (cpe,10). In this guide, only the values cpe,10 are taken into account, because they are used for the design of the overall load bearing structure of buildings.

Zones for vertical walls are defined in EN 1991-1-4 Figure 7.5 and the external pressure coefficients cpe,10 are given in EN 1991-1-4 Table 7.1. For intermediate values of h/d, linear interpolation may apply.

The values of the external pressure coefficients may be given in the National Annex.

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b

d

D E1

2 Plan

h A B C

e/5 4/5 e d e

1

h A B C 1

Elevation for e < d

h A B

e/5 d e/5

1

h A B1

Elevation for e d

1 Wind direction 2 Elevation

h A

d

1

h A 1

Elevation for e 5d

e = min(b ; 2h) b is the crosswind dimension

Figure 8.3 Key for vertical walls

For buildings with h/d > 5, the total wind loading may be determined by the force coefficients cf.

In cases where the wind force on building structures is determined by application of the pressure coefficient cpe on windward and leeward side (zones D and E) of the building simultaneously, the lack of correlation of wind pressures between the windward and leeward side may have to be taken into account as follows:

x For buildings with h/d 5, the resulting force is multiplied by 1 x For buildings with h/d 1, the resulting force is multiplied by 0,85 x For intermediate values of h/d, linear interpolation may be applied.

8.2.4 External pressure coefficients on roofs Zones for roofs and external coefficients cpe,10 attached to these zones are defined in EN 1991-1-4 as follows:

x Flat roofs: Figure 7.6 and Table 7.2 x Monopitch roofs: Figure 7.7 and Tables 7.3a and 7.3b x Duopitch roofs: Figure 7.8 and Tables 7.4a and 7.4b x Hipped roofs: Figure 7.9 and Table 7.5

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x Multispan roofs : Figure 7.10 and the coefficients cpe are derived from Tables 7.3 to 7.4.

Figure 8.4 of this guide shows the zones for duopitch roofs.

b

e/10

G

F

1

e/10

F

H J I

2 4

e/4

e/4

3

b

e/10

G

F

1

e/2

F

H I

I

2

e/4

e/4

G

H

Wind on the long side (perpendicular to the ridge line)

1 Wind direction 2 Ridge line 3 Upwind face 4 Downwind face

Wind on the gable (parallel to the ridge line)

e = min(b ; 2h) b is the crosswind dimension

Figure 8.4 Zones for duopitch roofs

8.2.5 Internal pressure coefficients The internal pressure coefficient cpi depends on the size and distribution of the openings in the building envelope.

When in at least two sides of the building (faades or roof) the total area of openings in each side is more than 30 % of the area of that side, the structure should be considered as a canopy roof and free-standing walls.

A face of a building should be regarded as dominant when the area of openings in that face is at least twice the area of openings in the remaining faces of the building considered.

Where an external opening would be dominant when open but is considered to be closed in the ultimate limit state, during severe windstorms (wind used for the design of the structure), the condition with the opening open should be considered as an accidental design situation.

For a building with a dominant face, the internal pressure should be taken as a fraction of the external pressure at the openings of the dominant face:

x Area of the openings on the dominant face = 2 u area of openings in the remaining faces: cpi = 0,75 cpe

x Area of the openings in the dominant face = 3 u area of openings in the remaining faces: cpi = 0,90 cpe

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x Area of the openings at the dominant face between 2 and 3 times the area of the openings in the remaining faces: Linear interpolation for calculating cpi.

When the openings are located in zones with different values of cpe, an area weighted average value should be used.

For buildings without a dominant face, the coefficient cpi should be determined from a function of the ratio h/d and the opening ratio P for each direction, as shown in Figure 8.5.

where: d

openings all of area 0 whereopenings of area

pec

Figure 8.5 Internal pressure coefficients for uniformly distributed openings

For values between h/d = 0,25 and h/d = 1,0, linear interpolation may be used.

Where it is not possible or not considered justified to estimate P for a particular case, then cpi should be taken as the more onerous of + 0,2 and 0,3.

The reference height zi for the internal pressures should be equal to the reference height ze for the external pressures on the faces which contribute by their openings to the creation of the internal pressure. Generally, for single-storey buildings, zi = ze = h and the velocity pressure qp(z): qp(zi) = qp(ze) = qp(h)

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8.3 Flowcharts

Fundamental value of the basic wind velocity vb,0

Construction location National map

Directional factor cdir Season factor cseason

Basic wind velocity vb

Terrain category

Roughness factor cr(z)

Peak velocity pressure qp(z)

Orography factor co(z)

Basic velocity pressure qb Air density U

Terrain factor kr

Turbulence factor kl

EN 1991-1-4 4.2(1)

(See National Annex)

EN 1991-1-4 4.5(1)

EN 1991-1-4 4.3.2

EN 1991-1-4 4.3.3 and A.3


EN 1991-1-4 4.4


Reference height z

EN 1991-1-4 4.5(1)

Figure 8.6 Flowchart A: calculation of the peak velocity pressure

Type of surface

External pressure coefficients cpe on vertical walls

Wind forces Fw,e and Fw,i

Peak velocity pressure qp(z)

Friction coefficient cfr Reference area Afr

External pressure coefficients cpe on roof

Internal pressure coefficients cpi

See Flowchart A

EN 1991-1-4 5.3

EN 1991-1-4 7.2.9

EN 1991-1-4 7.5

Table 7.10

EN 1991-1-4 7

Structural factor cs cd EN 1991-1-4

6 and Annexes B, C, D (See National Annex)

Friction forces Ffr EN 1991-1-4 5.3

Dimensions of the building

Figure 8.7 Flowchart B: Calculation of the wind forces

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9 EFFECT OF TEMPERATURE

Buildings not exposed to daily or seasonal climatic changes may not need to be assessed under thermal actions. For large buildings, it is generally good practice to design the building with expansion joints so that the temperature changes do not induce internal forces in the structure. Information about the design of expansion joints is given in Section 1.4.2 of Single-storey steel buildings Part 2: Concept design[11].

When the effects of temperature have to be taken into account, EN 1993-1-5 provides rules to determine them.

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REFERENCES 1 EN 1990:2002: Eurocode Basis of structural design

2 EN 1991-1-1:2002: Eurocode 1 Actions on structures. General actions. Densities, self-weight, imposed loads for buildings.

3 EN 1991-1-3:2003: Eurocode 1 Actions on structures. General actions. Snow loads

4 EN 1991-1-4:2005: Eurocode 1 Actions on structures. General actions. Wind actions

5 EN 1991-1-5:2003: Eurocode 1 Actions on structures. General actions. Thermal actions

6 EN 1991-3:2006: Eurocode 1 Actions on structures. Actions induced by cranes and machinery

7 CLAVAUD, D. Exemple de dtermination des charges de neige selon lEN 1991-1-3. Revue Construction Mtallique n2-2007. CTICM.

8 CLAVAUD, D. Exemple de dtermination des actions du vent selon lEN 1991-1-4. Revue Construction Mtallique n1-2008. CTICM.

9 EN 1998-1:2004: Eurocode 8 Design of structures for earthquake resistance. General rules, seismic actions and rules for buildings.

10 Steel Buildings in Europe Multi-storey steel buildings. Part 3: Actions

11 Steel Buildings in Europe Multi-storey steel buildings. Part 2: Concept design

Part 3: Actions

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Part 3: Actions

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APPENDIX A

Worked Example: Snow load applied on a single-storey building

3 - 36

APPENDIX A. Worked Example: Snow load applied on a single-storey building 1 of 8

Made by DC Date 02/2009

Calculation sheet Checked by AB Date 03/2009

1. Data This worked example deals with the single-storey building shown below.

B

A

A

25,00 m

B

Plan view

3,00 m

10%

25,00 m

15%

b2 = 10,00 m b1 = 40,00 m

1

1,25 m

6,00 m10,25 m

0,75 m

1

Cross-section BB Cross-section AA 1 Parapets Figure A.1 Geometry of the building

2. Snow load on the ground Characteristic value sk of snow load on the ground:

sk = 0,65 kN/m2

Coefficient for exceptional snow load:

Cesl = 2

EN 1991-1-3 4.3

Exceptional snow on the ground:

sAd = Cesl sk = 2 u 0,65 = 1,30 kN/m2

Title APPENDIX A. Worked Example: Snow load applied on a single-storey building 2 of 8

3 - 37

3. Snow load on the roof 3.1. General The loads act vertically and refer to a horizontal projection of the roof area.

Two primary load arrangements shall be taken account:

x undrifted snow load on roofs x drifted snow load on roofs

EN 1991-1-3 5.2(1)

Snow loads on roofs are determined as follows:

x Persistent (conditions of normal use)/transient (temporary conditions) design situations:

s = Pi Ce Ct sk

EN 1991-1-3 5.2(3) a)

x Accidental design situations (exceptional snow fall) where exceptional snow load is the accidental action:

s = Pi Ce Ct sAd

5.2(3) b)

x Accidental design situations (exceptional snow drift) where the accidental action is the exceptional drift and where Annex B applies:

s = Pi sk

5.2(3) c)

where:

Pi is the snow shape coefficient EN 1991-1-3 5.3

Ce is the exposure coefficient, Ce = 1,0 5.2(7)

Ct is the thermal coefficient, Ct = 1,0 5.2(8)

3.2. Upper roof (duo pitch roof) Angle of the roof (15%):

D = arc tan (0,15) = 8,5 0 d D d 30

x Persistent /transient design situations - Case (i) : undrifted load arrangement

P1(D = 8,5) = 0,8 s = 0,8 u 0,65 = 0,52 kN/m2

EN 1991-1-3 5.3.3 Figure 5.3

- Case (ii): Drifted load arrangement

0,5 P1 (D= 8,5) = 0,4 s = 0,4 u 0,65 = 0,26 kN/m2 - Case (iii): Drifted load arrangement

The case (iii) is symmetrical about the case (ii) because of the symmetry of the roof (D1 = D2 = 8,5).


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0,52 kN/m2

D

Case (i)

0,26 kN/m2 0,52 kN/m2

Case (ii)

0,52 kN/m2 0,26 kN/m2

Case (iii)

Figure A.2 Snow load arrangements on the upper roof in persistent design

situation

EN 1991-1-3 Figure 5.3

x Accidental design situations exceptional load on the ground - Case (i): Undrifted load arrangement

P1(D = 8,5) = 0,8 s = 0,8 u 1,30 = 1,04 kN/m2

- Case (ii): Drifted load arrangement

0,5 P1(D= 8,5) = 0,4 s = 0,4 u 1,30 = 0,52 kN/m2

- Case (iii): Drifted load arrangement The case (iii) is symmetrical about the case (ii) because of the

symmetry of the roof (D1 = D2 = 8,5)

1,04 kN/m2

D

Case (i)

0,52 kN/m2 1,04 kN/m2

Case (ii)

1,04 kN/m2 0,52 kN/m2

Case (iii)

Figure A.3 Snow load arrangements on the upper roof in accidental design

situation

x Accidental design situations exceptional drift: This case is not applicable. There are no parapets or valleys.


3 - 39

3.3. Lower roof: duo pitch roof abutting to taller construction works

Angle of the roof (10%):

D = arc tan (0,10) = 5,7 0 d D d 30

EN 1991-1-3 5.3.6(1)

x Persistent /transient design situations - Case (i): Undrifted load arrangement

P1(5,7) = 0,8 s = 0,8 u 0,65 = 0,52 kN/m2

0,52 kN/m2

0,52 kN/m2

Figure A.4 Undrifted snow load arrangement on the lower roof in persistent

design situation

- Case (ii): drifted load arrangement

P1(5,7) = 0,8 s = 0,8 u 0,65 = 0,52 kN/m2

P2 = Ps + Pw where:

Ps is the snow shape coefficient due to sliding of snow from the upper roof.

For D d 15: Ps = 0

Pw is the snow load shape coefficient due to wind Pw = (b1 + b2) / 2h with: Pw dJh/sk b1 = 10 m b2 = 40 m h varies between 3 m at ridge to 4,25 m at eaves

J = 2 kN/m3


3 - 40

The recommended range is: 0,8 d Pw d 4 At ridge: Jh/sk = 2 u 3/0,65 = 9,2 Pw = (10 + 40)/(2 u 3) = 8,3 d Jh/sk

At eave: Jh/sk = 2 u 4,25/0,65 = 13,1 Pw = (10 + 40)/(2 u 4,25) = 5,9 d Jh/sk But Pw should be maximum 4, so: Pw = 4

Therefore:

s = 4 u 0,65 = 2,60 kN/m2

ls is the drift length determined as: ls = 2h This drift length varies between 6 m at ridge to 8,50 m at eaves.

The recommended restriction is: 5 m ls 15 m

EN 1991-1-3 5.3.6(1)

2,60 kN/m26,00 m

8,50 m

2,60 kN/m2

0,52 kN/m20,52 kN/m2

Figure A.5 Drifted snow load arrangement on the lower roof in the case of

abutting to taller construction works in persistent design situation

EN 1991-1-3 Figure 5.7

x Accidental design situations exceptional load on the ground: - Case (i): Undrifted load arrangement

P1(5,7) = 0,8 s = 0,8 u 1,3 = 1,04 kN/m2

The arrangement is the same as Figure A.4 with: s = 1,04 kN/m2

- Case (ii): Drifted load arrangement The arrangement is the same as Figure A.5 with: s1 = 1,04 kN/m2


3 - 41

where:

P1 = 0,8 and s2 = 5,20 kN/m2 where Pw = 4

3.4. Lower roof: drifting at obstructions (parapets) Only persistent/transient design situations are to be considered.

Angle of the roof (10%): D = 5,7 P1(5,7) = 0,8 s = 0,8 u 0,65 = 0,52 kN/m2

EN 1991-1-3 6.2(2)

P2 = J h/sk where:

h is the height of parapet. It varies between 0 m at ridge and 1,25 m at low eaves.

J = 2 kN/m3 At ridge: P2 = 0 At low eaves: P2 = 2 u 1,25/0,65 = 3,8

With the restriction: 0,8 P2 2 ? P2 varies between 0,8 at ridge, and 2 at eave. s varies between 0,52 kN/m2 at ridge, and 2 u 0,65 = 1,30 kN/m2 at

low eaves.

The drift length ls is determined by: ls = 2 h This drift length varies between 0 m at ridge and 2,50 m at low eaves.

The recommended restriction is: 5 m ls 15 m. Therefore: ls = 5 m at low eaves.

5,00 m

5,00 m

0,52 kN/m2

5,00 m

1,30 kN/m2

0,52 kN/m20,52 kN/m2

1,30 kN/m2 1,30 kN/m2

5,00 m 5,00 m

Figure A.6 Drifted snow load arrangement on the lower roof in the case of

obstruction in persistent design situation


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3.5. Exceptional snow drifts

3.5.1. Roofs abutting and close to taller structures P1 = P2 = P3 = Min(2h/sk ; 2b/ls ; 8) where b is the larger of b1 or b2 ls = Min(5h ; b1 ; 15 m) h = 4,25 m b1 = 40,00 m b2 = 10,00 m sk = 0,65 kN/m2 5 h = 21,25m; ls = 15,00 m; 2h/sk = 13,08; 2b/ls = 5,3

? P1 = P2 = P3 = 5,3 And: s = P3 sk = 3,45 kN/m2

EN 1991-1-3 Annex B B.3

15,00 m

3,45 kN/m2

Figure A.7 Exceptional snow drifted on the lower roof in the case of roofs

abutting and close to taller building


3 - 43

3.5.2. Roofs where drifting occurs behind parapets at eaves P1 = Min(2 h/sk ; 2 b2/ls ; 8) where: ls = Min(5h ; b1 ; 15 m) h = 3,00 m b1 = 12,50 m b2 = 25,00 m sk = 0,65 kN/m2

5h = 15,00 m ; ls = 12,50 m ; 2h/sk = 9,23 ; 2b2/ls = 4,00

? P1 = 4,00 And: s = P1 sk = 2,60 kN/m2

EN 1991-1-3 Annex B B.4

3.5.3. Roofs where drifting occurs behind parapets at gable end P1 = Min(2 h/sk ; 2 b2/ls ; 8) where: ls = Min(5h ; b1 ; 15 m) h = 3,00 m b1 = 40,00 m b2 = 25,00 m sk = 0,65 kN/m2 5h = 15,00 m ; ls = 15,00m ; 2h/sk = 9,23 ; 2b2/ls = 5,33

? P1 = 5,33 And: s = P1 sk = 3,46 kN/m2

EN 1991-1-3 Annex B B.4

0,00 kN/m2

12,50 m 12,50 m

15,00 m

2,60 kN/m2 2,60 kN/m2

3,46 kN/m2

Snow behind the parapet at gable end Snow behind the parapets at eaves

Figure A.8 Exceptional snow drifted on the lower roof in the case of roofs where drifting occurs behind parapets at eaves

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Part 3: Actions

3 - 45

APPENDIX B

Worked Example: Wind action on a single-storey building

3 - 46

APPENDIX B. Worked Example: Wind action on a single-storey building 1 of 11

Made by DC Date 06/2009

Calculation sheet Checked by AB Date 07/2009

1. Data This worked example deals with the calculation of the wind action on a single-storey building according to EN 1991-1-4. The overall dimensions of the building are given in Figure B.1.

14

5 m

5 m

6 m

6 m 4,8 m

6 m

16 m

16 m 60 m

Figure B.1 Geometry of the building

The doors are assumed to be shut during severe gales.

The fundamental value of the basic wind velocity is:

vb,0 = 26 m/s

2. Peak velocity pressure The peak velocity pressure is determined according to the step-by-step procedure given in this guide.

1. Fundamental value of the basic wind velocity vb,0 = 26 m/s

2. Basic wind velocity For cdir and cseason, the recommended values are:

cdir = 1,0 cseason = 1,0

Then: vb = vb,0 = 26 m/s

EN 1991-1-4 4.2(2)

Title APPENDIX B. Worked Example: Wind action on a single-storey building 2

of 11

3 - 47

3. Basic velocity pressure

2b 2

1bvq U

where:

U = 1,25 kg/m3 (recommended value) Then: qb = 0,5 u 1,25 u 262 = 422,5 N/m2

EN 1991-1-4 4.5(1)

4. Terrain factor 07,0

II0,

0r 19,0

zzk

EN 1991-1-4 4.3.2(1) Table 4.1

The terrain category is category III, then:

z0 = 0,3 m zmin = 5 m

215,005,030,019,0

07,0

r

k

5. Roughness factor

0rr ln)( z

zkzc

z is taken equal to the height of the building: z = 8 m

Then: 706,03,00,8ln215,0)(r

u zc

EN 1991-1-4 4.3.2(1)

6. Orography factor The building is erected on a suburban terrain where the average slope of the upwind terrain is very low (< 3), so:

co(z) = 1

EN 1991-1-4 4.3.3(2)

7. Turbulence factor The recommended value is used:

kl = 1,0

EN 1991-1-4 4.4(1)


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3 - 48

8. Peak velocity pressure (alternative for a single-storey building) qp(z) = ce(z) qb where:

)( )()( )(

71)( 2r2o

ro

rle zczczczc

kkzc

EN 1991-1-4 4.5(1)

56,1706,00,1706,00,1

215,00,171)( 22e uu

uuu zc

Then: qp(z) = 1,56 u 423 = 659 N/m2 qp(z) = 0,659 kN/m2 for z = 8 m

3. Wind pressure on surfaces 3.1. External pressure coefficients cpe,10 3.1.1. Vertical walls

1. Wind on gable h = 8 m b = 32 m (crosswind dimension) h < b, so ze = reference height = h = 8 m

EN 1991-1-4 7.2.2 (1) Figure 7.4

d = 60 m h/d = 8/60 = 0,13 (h/d < 0,25)

EN 1991-1-4 7.2.2 (2) Table 7.1

2h = 16 m e = 16 m (b or 2h, whichever is smaller)

EN 1991-1-4 7.2.2 (1) Figure 7.5

e < d e/5 = 3,2 m 4/5 e = 12,8 m d e = 44 m

Figure B.2 defines the external pressure coefficients cpe,10 on vertical walls for zones A, B, C, D and E with wind on the gable.

EN 1991-1-4 7.2.2(2) Table 7.1


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+ 0,7 - 0,3

Wind

44 m

h = 8 m

3,2 m 12,8 m

- 0,5 - 0,8 - 1,2 DD

BB CCEE

AA

Figure B.2 cpe,10 for zones A, B, C, D and E with wind on gable

2. Wind on the long side h = 8 m b = 60 m (crosswind dimension) h < b, so ze = reference height = h = 8 m d = 32 m

EN 1991-1-4 7.2.2 (1) Figure 7.4

h/d = 8/32 = 0,25 2h = 16 m

EN 1991-1-4 7.2.2(2) Table 7.1

e = 16 m (b or 2h, whichever is smaller) e < d e/5 = 3,2 m 4/5 e = 12,8 m d e = 16 m

EN 1991-1-4 7.2.2(1) Figure 7.5

Figure B.3 defines the external pressure coefficients cpe,10 on vertical walls for zones A, B, C, D and E with wind on the long side.

EN 1991-1-4 7.2.2(2) Table 7.1


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h = 8 m

3,2 m

- 0,3+ 0,7 - 1,2

12,8 m

DD AA BB

EE- 0,8

16 m

CC

- 0,5

Wind

Figure B.3 cpe,10 for zones A, B, C, D and E with wind on long side

3.1.2. Roofs 1. Wind on gable

Ridges are parallel to the wind direction: T = 90 Pitch angle: D = 14 h = 8 m b = 32 m (crosswind dimension)

EN 1991-1-4 7.2.5(1) Figure 7.8

The reference height is: ze = h = 8 m 2h = 16 m

EN 1991-1-4 7.2.7(3)

e = 16 m (b or 2h, whichever is smaller) e/4 = 4 m e/10 = 1,6 m e/2 = 8 m

EN 1991-1-4 7.2.5(1) Figure 7.8

Figure B.4 defines the external pressure coefficients cpe,10 on roofs for zones F, G, H and I with a wind on gable.

EN 1991-1-4 7.2.2(2) Table 7b


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Trough

Ridge

- 1,3

- 1,3

- 0,6

- 0,6

- 1,3

Ridge

- 1,3

- 1,3

4 m

4 m

8 m

1,6 m

d = 60 m

- 1,3

- 0,6

Wind b = 32 m

- 0,5

- 0,5

- 0,6 - 0,5

- 0,5

FF

GG

GG

GG

II

II

II

II

HH

HH

HH

HH

GG

FF

Figure B.4 cpe,10 for zones F, G, H and I with wind on gable

2. Wind on long side

i. Ridges are perpendicular to the wind direction: T = 0 ii. Pitch angle D = 14 iii. h = 8 m iv. b = 60 m (crosswind dimension) v. h < b, so the reference height is: ze = h = 8 m

EN 1991-1-4 7.2.5(1) Figure 7.8

vi. d = 32 m vii. 2h = 16 m viii. e = 16 m (b or 2h, whichever is smaller) ix. e/4 = 4 m x. e/10 = 1,6m

EN 1991-1-4 7.2.5(1) Figure 7.8

Figure B.5 defines the external pressure coefficients cpe,10 on roofs for zones F, G, H, I and J with a wind on long side.

EN 1991-1-4 7.2.7(2) Figure 7.10c


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Trough

Trough

- 0,9+ 0,2 - 0,8

+ 0,2

- 0,5

- 0,9 + 0,2

Ridge

1,6 m

4 m4 m

b = 60 m

Wind

d = 32 m

- 0,3 + 0,2

- 0,5 HH

HH

GG

FF FF

HH - 0,9

II

Figure B.5 cpe,10 for zones F, G, H and I with wind on long side

3.2. Internal pressure coefficients cpi 3.2.1. Persistent or transient design situation

The doors are assumed to stay shut during severe gales:

cpi = + 0,2 And cpi = -0,3 with reference height for the internal pressure: zi = ze = h = 8 m

EN 1991-1-4 7.2.9(6) 7.2.9(7)

3.2.2. Accidental design situation

x A door opens upwind (wind on gable): this face is dominant and area of the openings at the dominant face = 3 u area of the openings in the remaining faces:

cpi = 0,90 cpe cpi = 0,90 u (+0,7) = +0,63 x A door opens downwind (wind on long side): this face is dominant and

area of the openings at the dominant face = 3 u area of openings in the remaining faces.

EN 1991-1-4 7.2.9(3) 7.2.9(5)


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The most severe case is when the opening is in a zone where |cpe| is the highest (the door is completely in zone B).

cpi = 0,90 cpe

cpi = 0,90 u -0,8 = -0,72

EN 1991-1-4 7.2.9(6)

4. Friction forces 4.1. Wind on gable

The area of the external surfaces parallel to the wind is calculated by:

60 u 2 u (6 + 8,25 u 2) = 2700 m2 The area of the external surfaces perpendicular to the wind is:

2 u 2 u 16 u (6 + 1) = 448 m2

The area of the external surfaces parallel to the wind is higher than 4 u area of external surfaces perpendicular to the wind: friction forces should be taken into account:

EN 1991-1-4 5.3(4)

4 h = 32 m 2 b = 64 m

4 h < 2 b The friction forces apply on the area Afr:

Afr = 2 u (60 32) u (6 + 8,25 u 2) = 1260 m2

EN 1991-1-4 7.5(3)

For a smooth surface (steel):

cfr = 0,01 and the friction force Ffr (acting in the direction of the wind):

Ffr = cfr qp(ze) Afr = (0,01 u 66 u 1260) 10-2 = 8,316 kN

EN 1991-1-4 5.5(3)

4 h < 2 b The friction forces apply on the area Afr:

Afr = 2 u (60 32) u (6 + 8,25 u 2) = 1260 m2

EN 1991-1-4 7.5(3)

For a smooth surface (steel):

cfr = 0,01 and the friction force Ffr (acting in the direction of the wind):

Ffr = cfr qp(ze) Afr = (0,01 u 66 u 1260) 10-2 = 8,316 kN

EN 1991-1-4 5.5(3)

4.2. Wind on long side Area of external surfaces parallel to the wind < 4 u area of external surfaces perpendicular to the wind: friction forces should not be taken account

EN 1991-1-4 5.3(4)


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5. Wind forces on surfaces F/Aref = cscd qp(ze) cpe qp(zi) cpi with: cscd = 1 (height < 15 m)

qp(ze) = qp(zi) = 0,66 kN/m2 The figures below show the wind forces per unit surfaces:

F/Aref = 0,66 (cpe cpi) (in kN/m2)

EN 1991-1-4 6.2(1)b

Wind

+0,33

-0,99 -0,53

-0,46

-0,33

-0,92

-0,66

-0,46

Ffr = 8,32 kN

Figure B.6 Wind on gable with cpi = +0,2

Wind

+0,66

-0,66 -0,20

-0,13

0

-0,59

-0,33

-0,13

Ffr = 8,32 kN

Figure B.7 Wind on gable with cpi = -0,3


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-0,73

Wind

+0,33

-0,73 (+ 0)

-0,33(+ 0)

-0,46 -0,33

-0,92

-0,66

-0,46 -0,73(+ 0)

-0,66(+ 0)

Figure B.8 Wind on long side with cpi = +0,2

The values in brackets should be used together.

Wind

+0,66

-0,40 (+0,33)

-0 (+0,33)

-0,13

0

-0,59

-0,33

-0,13 -0,40(+0,33)

-0,33(+0,33)

-0,40

Figure B.9 Wind on long side with cpi = -0,3

Values in brackets should be used together.


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Wind

+0,07

-1,25 -0,79

-0,73

-0,59

-1,19

-0,92

-0,73

Ffr = 8,32 kN

Figure B.10 Accidental design situation: door open upwind (wind on gable)

with cpi = +0,6

Wind

+0,92

-0,13 (+0,59)

-0,26(+0,59)

+0,13 +0,26

-0,33

-0,7

+0,13 -0,13 (+0,59)

-0,07(+0,59)

+0,13

Figure B.11 Accidental design situation: door open downwind (wind on long

side) with cpi = -0,7

Values in brackets should be used together

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